Finite Element Analysis of A Slip Casting Process of Slurry Based on Three Dimensional Filtration Theory

本文的主要研究成果如下：(1)将现代过滤理论推广到广义坐标系，建立了三维滑移浇铸过程的基本方程组。它由包含液体流速q和固体迁移速率r的基本流速方程，以及向量q和r的散度与孔隙度随时间变化的连续性方程，以及液体压力p_L与固体压缩压力p_S的关系组成。假设q和r的方向与-∇p_L=∇p_S重合，并借助压缩渗透率(CP)-特征，最终得到两个偏微分方程。在空间上用伽辽金有限元法离散，在时间上用有限差分法离散，在每个时间增量上用高斯消去法求解得到的矩阵方程。考虑主曲率的影响，计算了饼面和液面。圆柱型石膏模内滑移铸件的数值计算结果表明，该方法不仅可以预测铸坯的三维生长，还可以预测孔隙率、压力、流量等内部条件的时间演变，并进一步预测浆液浓度的影响。(2)采用较大过滤介质阻力Rm的单次恒压过滤初始阶段滤液体积V与时间θ的关系，提出了一种简单的预测压缩渗透率（CP）特性的方法。为了利用现代滤波理论和单纯形法使计算的（V vs.θ）关系与观测值的偏差最小，对CP-和rm -特性的十个参数进行了搜索。在高岭土料浆体系中的应用表明，该方法能快速、准确地测定高岭土料浆的CP-特性。

The main results of the present study are as follows :(1) Fundamental equation set governing three-dimensional slip casting process is proposed by extending modern filtration theory to generalized coordinate system. It consists of a basic flow rate euation, which contains the liquid velocity q and the solid migration rate r, and the continuity equations relating the divergence of vectors q and r to porosity variation with time, and a relationship between liquid pressure p_L and solid compressive pressure p_S Assuming that the direction of q and r coincide with -∇p_L=∇p_S and with the aids of compression permeability (CP)-characteristics, two partial differential equations are finally reduced. These equations were discretized with a Galerkin finite element method in space and with a finite difference method in time, and resultant matrix equations were solved using the Gauss elimination method at each time increment. Cake surface and liquid front were computed considering the effect of principal curvatures. The numerical results of slip castings in a cylindrical plaster mold showed that the proposed method enables the prediction of not only three dimensional cake growth but also time evolution of various internal conditions, such as porosity, pressure and flow rates, and further the effect of slurry concentration.(2) A simple predictive method to determine compression permeability (CP)-characteristics are proposed, using the filtrate volume V vs. the time θ relation in the initial stage of a single constant pressure filtration run with a relatively large filter medium resistance Rm. Ten parameters, for specifing the CP- and Rm-characteristics, are searched so as to minimize the deviation of computed (V vs.θ) relation from observed one using modern filtration theory and Simplex method. Application to a Kaolin slurry system showed that the proposed method enables the rapid determination of CP- characteristics with high accuracy.